3(x/2+1)-16=3/2x

Solution for 3(x/2+1)-16=3/2x equation:

3(x/2+1)-16=3/2x

We move all terms to the left:

3(x/2+1)-16-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x/2+1)-(+3/2x)-16=0

We multiply parentheses

3x-(+3/2x)+3-16=0

We get rid of parentheses

3x-3/2x+3-16=0

We multiply all the terms by the denominator


3x*2x+3*2x-16*2x-3=0

Wy multiply elements

6x^2+6x-32x-3=0

We add all the numbers together, and all the variables

6x^2-26x-3=0

a = 6; b = -26; c = -3;
Δ = b2-4ac
Δ = -262-4·6·(-3)
Δ = 748
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{187}}{2*6}=\frac{26-2\sqrt{187}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{187}}{2*6}=\frac{26+2\sqrt{187}}{12}
$